Properties

Level $14$
Weight $0$
Character 14.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 14 = 2 \cdot 7 \)
Weight: \( 0 \)
Character: 14.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 7.82039168819 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.212262974\) \(a_{4}=+0.500000000\) \(a_{5}=+1.643693228\)
\(a_{6}=-0.150092588\) \(a_{7}=+0.377964473\) \(a_{8}=-0.353553391\) \(a_{9}=-0.954944430\) \(a_{10}=-1.162266628\)
\(a_{11}=+0.006941887\) \(a_{12}=+0.106131487\) \(a_{13}=+1.044023766\) \(a_{14}=-0.267261242\) \(a_{15}=+0.348895212\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.344163960\) \(a_{18}=+0.675247682\) \(a_{19}=-0.627332684\) \(a_{20}=+0.821846614\)
\(a_{21}=+0.080227863\) \(a_{22}=-0.004908655\) \(a_{23}=+1.844775027\) \(a_{24}=-0.075046294\) \(a_{25}=+1.701727427\)
\(a_{26}=-0.738236285\) \(a_{27}=-0.414962318\) \(a_{28}=+0.188982237\) \(a_{29}=-1.570522142\) \(a_{30}=-0.246706171\)
\(a_{31}=+1.239862851\) \(a_{32}=-0.176776695\) \(a_{33}=+0.001473506\) \(a_{34}=-0.243360670\) \(a_{35}=+0.621257645\)
\(a_{36}=-0.477472215\) \(a_{37}=+0.765282245\) \(a_{38}=+0.443591195\) \(a_{39}=+0.221607589\) \(a_{40}=-0.581133314\)
\(a_{41}=+0.617086968\) \(a_{42}=-0.056729666\) \(a_{43}=+1.496377064\) \(a_{44}=+0.003470944\) \(a_{45}=-1.569635693\)
\(a_{46}=-1.304452932\) \(a_{47}=-0.088805837\) \(a_{48}=+0.053065743\) \(a_{49}=+0.142857143\) \(a_{50}=-1.203303004\)
\(a_{51}=+0.073053266\) \(a_{52}=+0.522011883\) \(a_{53}=+1.215019510\) \(a_{54}=+0.293422669\) \(a_{55}=+0.011410333\)
\(a_{56}=-0.133630621\) \(a_{57}=-0.133159501\) \(a_{58}=+1.110526857\) \(a_{59}=-0.351888321\) \(a_{60}=+0.174447606\)
\(a_{61}=-0.666259248\) \(a_{62}=-0.876715430\) \(a_{63}=-0.360935068\) \(a_{64}=+0.125000000\) \(a_{65}=+1.716054794\)
\(a_{66}=-0.001041926\) \(a_{67}=+0.009352958\) \(a_{68}=+0.172081980\) \(a_{69}=+0.391577433\) \(a_{70}=-0.439295493\)
\(a_{71}=-0.156493657\) \(a_{72}=+0.337623841\) \(a_{73}=-1.747155891\) \(a_{74}=-0.541136265\) \(a_{75}=+0.361213724\)
\(a_{76}=-0.313666342\) \(a_{77}=+0.002623787\) \(a_{78}=-0.156700229\) \(a_{79}=-0.048806362\) \(a_{80}=+0.410923307\)
\(a_{81}=+0.866863294\) \(a_{82}=-0.436346380\) \(a_{83}=+0.161227832\) \(a_{84}=+0.040113931\) \(a_{85}=+0.565699970\)
\(a_{86}=-1.058098369\) \(a_{87}=-0.333363700\) \(a_{88}=-0.002454328\) \(a_{89}=+0.146957178\) \(a_{90}=+1.109900042\)
\(a_{91}=+0.394603893\) \(a_{92}=+0.922387514\) \(a_{93}=+0.263176976\) \(a_{94}=+0.062795210\) \(a_{95}=-1.031142484\)
\(a_{96}=-0.037523147\) \(a_{97}=+0.699114160\) \(a_{98}=-0.101015254\) \(a_{99}=-0.006629116\) \(a_{100}=+0.850863714\)

Showing 100 of 190 available coefficients

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